We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characteriza...We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.展开更多
In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the result...In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.展开更多
In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz’s inequality is pro...Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz’s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic.展开更多
In this paper,we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.
The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential...The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential perspective of each monad＇s extrinsic denominators. This is attained by a thorough explication of the principle of indiscernibles, the abolition of the principle of locality, the advanced conception ofentelecheia in late Leibniz, and the character of the perception of each monad, which allow to discover in Leibniz＇s idea of space the notion of the hologram, and the holographic interconnectedness of things in the Universe.展开更多
A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
Viewing gravitational energy momentum as equal by observation, but different in essence from inertial energy-momentum requires two different symmetries to account for their independent conservations—spacetime and inn...Viewing gravitational energy momentum as equal by observation, but different in essence from inertial energy-momentum requires two different symmetries to account for their independent conservations—spacetime and inner translation invariance. Gauging the latter a generalization of non-Abelian gauge theories of compact Lie groups is developed resulting in the gauge theory of the non-compact group of volume-preserving diffeomorphisms of an inner Minkowski space M4. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws for the new gauge theory are developed. Finally, the theory’s Hamiltonian in the axial gauge is expressed by two times six unconstrained independent canonical variables obeying the usual Poisson brackets and the positivity of the Hamiltonian is related to a condition on the support of the gauge fields.展开更多
2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the...2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.展开更多
The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive m...The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.展开更多
文摘We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.
基金Project supported by the Natural Science Foundation of Yibin University (No. 2009Z01)
文摘In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.
文摘In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
基金The NNSF (10271053) of China and the Science Foundation (HGDJJ03001) of Naval University of Engineering.
文摘Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz’s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic.
文摘In this paper,we obtain some new fixed point theorems in fuzzy-Banach spaces by considering the t-norms of h-type and a linear mapping of weakly demicompact.
文摘The paper provides an interpretation of Leibniz＇s account of space that extends beyond the predominant interpretations in terms of the relativity of space, and the latter is mainly understood through the differential perspective of each monad＇s extrinsic denominators. This is attained by a thorough explication of the principle of indiscernibles, the abolition of the principle of locality, the advanced conception ofentelecheia in late Leibniz, and the character of the perception of each monad, which allow to discover in Leibniz＇s idea of space the notion of the hologram, and the holographic interconnectedness of things in the Universe.
文摘A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.
文摘Viewing gravitational energy momentum as equal by observation, but different in essence from inertial energy-momentum requires two different symmetries to account for their independent conservations—spacetime and inner translation invariance. Gauging the latter a generalization of non-Abelian gauge theories of compact Lie groups is developed resulting in the gauge theory of the non-compact group of volume-preserving diffeomorphisms of an inner Minkowski space M4. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws for the new gauge theory are developed. Finally, the theory’s Hamiltonian in the axial gauge is expressed by two times six unconstrained independent canonical variables obeying the usual Poisson brackets and the positivity of the Hamiltonian is related to a condition on the support of the gauge fields.
文摘2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.
文摘The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
